Geodesic
Iterative method for solving a non-linear edge problems with a point source
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 74-79

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In this paper, we consider the first boundary value problem for a quasilinear equation in a bounded domain with a point source. The solution of the problem is sought in the form of the sum of three functions. The first function is represented explicitly and is the solution of a linear equation with a point source with constant coefficients. The second function is found from the solution of a linear homogeneous boundary value problem with constant coefficients. To search for the third function an iterative process is used that converges strongly in the Sobolev space at the rate of a geometric progression.
Mots-clés : point source
Keywords: non-linear boundary value problem, iterative process. 
@article{IVM_2022_5_a5,
     author = {O. A. Zadvornov and G. O. Trifonova},
     title = {Iterative method for solving a non-linear edge problems with a point source},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--79},
     publisher = {mathdoc},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_5_a5/}
}
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O. A. Zadvornov; G. O. Trifonova. Iterative method for solving a non-linear edge problems with a point source. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 74-79. http://geodesic.mathdoc.fr/item/IVM_2022_5_a5/